Question

Find the area of a circle whose circumference is the same as the perimeter of a square of side 11cm

Answer 1

your question answer is = 154 CM 2

Answer 2

$\bold{154.12 \mathrm{cm}^{2}}$ is the area of a circle whose perimeter of a square of side 11 cm.

Given:

Side of a square is 11cm  

Circumference of a circle = perimeter of square

To find:

Area of the circle?

Solution:

We know that the circumference of the circle $=2 \pi r$

Where r is the radius of the circle.

Perimeter of the square = sum of the sides of the square = 4s where s is the side of the square.So,perimeter$=4 \times 11=44 \mathrm{cm}$

As perimeter = area of the circle  

$\begin{array}{l}{\Rightarrow 44=2 \times \pi \times r} \\ {\Rightarrow r=\frac{44}{2 \times 3.14}} \\ {\Rightarrow r=\frac{22}{3.14}} \\ {\Rightarrow r=7.006}\end{array}$

Now, area of the circle

$= \begin{array}{l}{=\pi \times r^{2}} \\ {3.14 \times 7.006^{2}} \\ {=154.12 \mathrm{cm}^{2}}\end{array}$

Area of the circle $\bold{=154.12 \mathrm{cm}^{2}}$